a screen is placed 90cm from an object. the image of an object on the screen is formed by a convex lens at two different locations separated by 20cm. the focal length of the lens is?

							If the object has two images then the object is placed at the focus and the emergent rays are parallel to the principal axis. Imagine a point object in front of a convex lens.Now two light rays emerge from the object each one is refracted in such a way that they become parallel to the principal axis.Now these two rays hit the screen and appear as two different images. thus it is safe to say that the focal length  is equal to the object distance i.e. 90 cm. Please verify this answer. I hope this was at least a little helpful.
						

							
1/f=1/v-1/u at position 1
1/f=(1/v-20)-(1/u+20)
1/v-1/u=(1/v-20)-(1/u+20)
solve it and get the answer
answer is 21.4cm
						

							
use the formula, f=D^2-d^2/4D,where D=100cm and d= 20cm.
Now,by putting the values of d and D in the above formula ,calculate the focal length.
						

							Distance from object to screen is 90u+v=90; difference in location of lens is 20So u-v=20......by solving we get u= 35 or 55 and v=55 or 35Then by using lens formula f=21.38 cm